Both sides said that the U.S. and Israel are near an agreement on a halt to expanding Israeli settlements on disputed territory. If Netanyahu approves, U.S. officials said, it could re-open direct negotiations between Israeli and Palestinian leaders on Mideast peace for the first time since before Israeli’s invasion of Gaza last winter.

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But the Israeli premier and the American president have gotten off on uncertain footing, with neither proving as willing to make early compromises as the other expected. The relationship is important to both leaders’ domestic politics, and now U.S. officials say the settlement negotiations give Netanyahu a way to show he’s committed to the Mideast peace process.

"Netanyahu’s at a pivotal moment,” said a senior U.S. official. “Depending on what he decides, he could wind up with a very strong relationship with President Obama and potentially become a historic figure in Israel."

“It could very well hinge on what he decides in the next couple of weeks,” said the official, who spoke on the condition of anonymity.

Another senior U.S. official held out a similar carrot for Netanyahu: This moment offers the opportunity to “forge a very important and positive relationship between Netanyahu and the president,” the official said.

Netanyahu spokesman Ron Dermer declined to comment on the Americans’ characterization, but Israel has been reluctant to cast settlements as a central question in the peace process, and another senior Israeli government official downplayed the importance of a deal this month.

The White House, however, is eager for its first diplomatic breakthrough in the Middle East, and the intense focus on the conservative Israeli leader comes as Israeli negotiators hold a new round of meetings in the United States.

Netanyahu envoy Yitzhak Molcho and Israeli Defense Ministry Chief of Staff Michael Herzog met White House officials, including National Security Council senior directors Dennis Ross and Dan Shapiro, in Washington Tuesday. They’re scheduled meet Special Envoy George Mitchell and his team in New York Wednesday.

Mitchell plans to return to the region next week, and officials are tentatively planning a meeting on the sidelines of the U.N. General Assembly later this month between Obama, Netanyahu, and Palestinian Authority President Mahmoud Abbas.

"President Obama will chair it, and I think that at least there is a chance that they will decide they are going to reopen negotiations,” Israeli President Shimon Peres told Fox News Monday, though U.S., Israeli, and Palestinian officials all said that plans for a trilateral meeting will depend on the outcome of the talks between the U.S. and Israel.

“There hasn’t been any official invitation,” said the chief of the Palestinian mission to Washington, Maen Areikat.

The American focus, for the present, is Netanyahu. Officials on both sides familiar with the talks said that the American and Israeli sides appear close to compromise on two crucial issues: The U.S. may agree to let Israel complete the construction of buildings that are already underway in the disputed territories; and Israel – which has refused to include disputed Jerusalem neighborhoods in the settlement talks — appears willing to forswear evictions and demolitions in the Palestinian parts of Jerusalem.

“The Israelis have asked for us to let them finish existing construction,” said the U.S. official. “We’ve made clear that we need some commitments on evictions and demolitions in Jerusalem.”

One outstanding issue, another person familiar with the talks said: What happens if talks fail. Israel would like a formal acknowledgement that it can resume building if, after six or nine months, talks have fallen apart. The U.S. side says it won’t offer formal sanction to settlements that it has always opposed.

Still, American and Israeli officials this week are sounding a new, more optimistic tone that the talks on settlements will be resolved, perhaps during Mitchell’s trip next week.

“We’re really on the verge of something really positive happening, We basically know what an agreement looks like and we’re close to it,” said the second senior U.S. official. “There’s a lot at stake, in both the relationship terms and the substance of the peace effort.”

American officials say the White House is pleased with Palestinian progress on West Bank security issues, and a series of confidence-building measures from Arab states, including direct air travel, over-flights and economic cooperation.

A senior Israeli government official, who also spoke on the condition of anonymity, also cited “optimism on both sides that this thing can be wrapped up.”

But while the Americans expressed optimism at the prospect of a dramatic first step, the administration’s accomplishment would simply be to re-open talks – not necessarily to close the wide gap that remains between the two sides, and officials on both sides stressed the distance yet to be traveled. Core questions like the status of Jerusalem, the location of borders, Israel’s security, and the place of Palestinian refugees remain unaddressed.

Israeli officials say settlements are a mere side issue, and that Netanyahu’s place in history will ride on more central questions, like his insistence that Palestinian leaders accept Israel as a Jewish state. And they doubt their counterparts’ readiness to deal.

The Palestinians at a recent Fatah conference were “engaging in extremist rhetoric, taking extreme positions on final status issues,” said the Israeli government official. “We’re skeptical about their willingness really to move forward.”

Palestinians, too, doubt Israel’s willingness to compromise.

“We are encouraged by the level of activity that this administration is undertaking, but at the same time we believe that in the process we should continue to focus on also the endgame,” said Areikat. “Even if the United States manages to get an agreement with Israel on a settlement freeze – what is the next step?”

Analysts say a handshake between Netanyahu and Obama on settlement talks would be an important step – but only the first one.

“What we’re talking about right now is a transactional arrangement – we’re just talking about the beginnings of negotiations,” said Aaron David Miller, a former American peace negotiator and a fellow at the Woodrow Wilson Center for Scholars. “This is going to be like a thousand days of root canals, every day, because it’s going to be excruciatingly painful to move this forward.”